What is the general solution for 6sin(x)+4cos(x)=0 ?

The general solution for 6sin(x)+4cos(x)=0 is x=-0.58800…+pin

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6sin(x)+4cos(x)=0

6 sin (x) + 4 cos (x) = 0

x = - 0.58800 \dots + πn

Degrees

x = - 33.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

6 sin (x) + 4 cos (x) = 0

Rewrite using trig identities

6 sin (x) + 4 cos (x) = 0

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{6 sin ( x ) + 4 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{6 sin ( x )}{cos ( x )} + 4 = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

6 tan (x) + 4 = 0

6 tan (x) + 4 = 0

Move

4

to the right side

6 tan (x) + 4 = 0

Subtract

4

from both sides

6 tan (x) + 4 - 4 = 0 - 4

Simplify

6 tan (x) = - 4

6 tan (x) = - 4

Divide both sides by

6

6 tan (x) = - 4

Divide both sides by

6

\frac{6 tan ( x )}{6} = \frac{- 4}{6}

Simplify

\frac{6 tan ( x )}{6} = \frac{- 4}{6}

Simplify

\frac{6 tan ( x )}{6} : tan (x)

\frac{6 tan ( x )}{6}

Divide the numbers:

\frac{6}{6} = 1

= tan (x)

Simplify

\frac{- 4}{6} : - \frac{2}{3}

\frac{- 4}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{6}

Cancel the common factor:

2

= - \frac{2}{3}

tan (x) = - \frac{2}{3}

tan (x) = - \frac{2}{3}

tan (x) = - \frac{2}{3}

Apply trig inverse properties

tan (x) = - \frac{2}{3}

General solutions for

tan (x) = - \frac{2}{3}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{2}{3}) + πn

x = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

x = - 0.58800 \dots + πn

cos (t) + sin (t) = 0

cos (C) = 0.87

4 cot (x) + 3 = - 1

cos (\frac{θ}{2}) - cos (θ) = 1

cot (θ) = \frac{4}{3}

What is the general solution for 6sin(x)+4cos(x)=0 ?
The general solution for 6sin(x)+4cos(x)=0 is x=-0.58800…+pin